Adrien Broner did not back out of an NYC event to promote his fight over threats made by East Coast rapperTekashi69 … at least that’s what Showtime tells TMZ Sports.

Broner was supposed to attend an open workout on Wednesday to drum up publicity for his fight with Jessie Vargas … but those plans were abruptly scrapped earlier this week.

And since Broner and Tekashi have been at war on social media, some people wondered if Broner feared the feud was about to turn violent since Tekashi claims to be a well-connected Blood … especially in NYC.

But a rep for Showtime Sports tells us that’s simply not the case … Broner didn’t back out of anything — instead, Showtime’s team changed the publicity strategy and canceled the workout for other media events.

Still, don’t expect the feud to die down anytime soon … these guys HATE each other.